Problem: $f(x) = \dfrac{ x + 9 }{ ( x + 9 )( x - 7 ) }$ What is the domain of the real-valued function $f(x)$ ?
$f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-9$ or $x=7$ So we know that $x \neq -9$ and $x \neq 7$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-9, \,x \neq7\, \}$.